Python Program to Find Sum of Series 1/2-2/3+3/4-4/5+5/6...+N/N+1

In the previous article, we have discussed Python Program to Find Sum of Series (1+(1*2)+(1*2*3)+…till N)

Given a number N and the task is to find the sum of the given series (1/2-2/3+3/4-4/5+5/6…+N/N+1) for the given number in Python.

Examples:

Example1:

Input:

Given Number = 17

Output:

The total sum of the series till the given number { 17 } =  0.6661398242280596

Example2:

Input:

Given Number = 6

Output:

The total sum of the series till the given number { 6 } =  -0.2404761904761904

Program to Find Sum of Series 1/2-2/3+3/4-4/5+5/6…+N/N+1 in Python

Below are the ways to find the sum of the given series (1/2-2/3+3/4-4/5+5/6…+N/N+1) for the given number in Python :

Using While Loop (Static Input)
Using While loop (User Input)

Method #1: Using While Loop (Static Input)

Approach:

Give the number N as static input and store it in a variable.
Take a variable say resltsum which gives the sum of the given series till N and initialize its value to 0.0 (floating number).
Take another variable say k and initialize its value with 1.
Loop until the value of k is less than or equal to the given number using the while loop.
Check if the value k modulus 2 is even or not using the if conditional statement.
If the statement is True, then subtract k/(k+1) from the above-declared resltsum.
Store it in the same variable resltsum.
Else if the statement is False, then add k/(k+1) to the above-declared resltsum.
Store it in the same variable resltsum.
Increment the value of k by 1 and store it in the same variable k.
Print the resltsum value which is the result of the series till the given Number N.
The Exit of the Program.

Below is the implementation:

# Give the number N as static input and store it in a variable.
gvn_numb = 17
# Take a variable say resltsum which gives the sum of the given series till N and
# initialize its value to 0.0 (floating number).
resltsum = 0.0
# Take another variable say k and initialize its value with 1.
k = 1
# Loop until the value of k is less than or equal to the given number using the while loop.
while(k <= gvn_numb):
    # Check if the value k modulus 2 is even or not using the if conditional statement.
    if(k % 2 == 0):
        # If the statement is True, then subtract k/(k+1) from the above-declared resltsum.
        # Store it in the same variable resltsum.
        resltsum -= k/(k+1)
    else:
      # Else if the statement is False, then add k/(k+1) to the above-declared resltsum.
       # Store it in the same variable resltsum.
        resltsum += k/(k+1)
 # Increment the value of k by 1 and store it in the same variable k.
    k += 1
# Print the resltsum value which is the result of the series till the given Number N.
print(
    "The total sum of the series till the given number {", gvn_numb, "} = ", resltsum)

Output:

The total sum of the series till the given number { 17 } =  0.6661398242280596

Method #2: Using While loop (User Input)

Approach:

Give the number N as user input using the int(input()) function and store it in a variable.
Take a variable say resltsum which gives the sum of the given series till N and initialize its value to 0.0 (floating number).
Take another variable say k and initialize its value with 1.
Loop until the value of k is less than or equal to the given number using the while loop.
Check if the value k modulus 2 is even or not using the if conditional statement.
If the statement is True, then subtract k/(k+1) from the above-declared resltsum.
Store it in the same variable resltsum.
Else if the statement is False, then add k/(k+1) to the above-declared resltsum.
Store it in the same variable resltsum.
Increment the value of k by 1 and store it in the same variable k.
Print the resltsum value which is the result of the series till the given Number N.
The Exit of the Program.

Below is the implementation:

# Give the number N as user input using the int(input()) function and
# store it in a variable.
gvn_numb = int(input("Enter some Random Number = "))
# Take a variable say resltsum which gives the sum of the given series till N and
# initialize its value to 0.0 (floating number).
resltsum = 0.0
# Take another variable say k and initialize its value with 1.
k = 1
# Loop until the value of k is less than or equal to the given number using the while loop.
while(k <= gvn_numb):
    # Check if the value k modulus 2 is even or not using the if conditional statement.
    if(k % 2 == 0):
        # If the statement is True, then subtract k/(k+1) from the above-declared resltsum.
        # Store it in the same variable resltsum.
        resltsum -= k/(k+1)
    else:
      # Else if the statement is False, then add k/(k+1) to the above-declared resltsum.
       # Store it in the same variable resltsum.
        resltsum += k/(k+1)
 # Increment the value of k by 1 and store it in the same variable k.
    k += 1
# Print the resltsum value which is the result of the series till the given Number N.
print(
    "The total sum of the series till the given number {", gvn_numb, "} = ", resltsum)

Output:

Enter some Random Number = 6
The total sum of the series till the given number { 6 } = -0.2404761904761904

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